I have heard that Botox can help prevent or reduce future lines and wrinkles. How does that work?

Botox acts by relaxing the muscles.  If a muscle does not fully contract, the skin over the muscle does not wrinkle.  Repeated contractions of the muscles can cause deep wrinkles in the skin, which eventually will produce a permanent crease.  After that happens, even Botox will not fully eliminate the crease.  If Botox is injected at the first sign of wrinkling, a deep crease will never develop.